Cross Validate Strategy
Kevin Lu
October 17, 2017
1. Load Packages
source("./Mean Reversion/RMR.001 Load Packages.R") 2. Load Data
pricing_data <- read_csv("./Mean Reversion/Raw Data/pricing data.csv") ## Parsed with column specification:
## cols(
## date_unix = col_integer(),
## date_time = col_datetime(format = ""),
## high = col_double(),
## low = col_double(),
## open = col_double(),
## close = col_double(),
## volume = col_double(),
## quote_volume = col_double(),
## weighted_average = col_double(),
## currency_pair = col_character(),
## period = col_integer()
## )3. Prepare Data Function
Description
Spreads Poloneix pricing data into wide format and filters data to a specified time resolution and time window.
Arguments
pricing_data: A dataframe containing pricing data from Poloneix gathered in tidy format.
time_resolution: The number of seconds that each observation spans. Takes values 300, 900, 1800, 7200, 14400, and 86400.
start_date: The start date of the time window.
end_date: The end date of the time window.
prepare_data <- function(pricing_data, time_resolution, start_date, end_date) {
df <- pricing_data %>%
filter(period == time_resolution,
date_time >= start_date,
date_time <= end_date) %>%
select(date_unix, date_time, close, currency_pair) %>%
spread(currency_pair, close)
return(df)
} 4. Test Cointegration Function
Description
The Engle-Granger method is used to test for cointegration. This method is comprised of two steps: (1) Perform a linear regression of log(coin_y) on log(coin_x). (2) Perform an Augmented Dickey-Fuller test on the residuals from the linear regression estimated in (1). The ADF test specification is of a non-zero mean, no time-based trend, and one autoregressive lag. The function returns the ADF test statistic.
Arguments
coin_y: A vector containing the pricing data for the dependent coin in the regression.
coin_x: A vector containing the pricing data for the independent coin in the regression.
test_cointegration <- function(coin_y, coin_x) {
lm_model <- lm(log(coin_y) ~ log(coin_x))
lm_residuals <- lm_model[["residuals"]]
adf_test <- ur.df(lm_residuals, type = "drift", lags = 1)
df_stat = adf_test@testreg[["coefficients"]][2, 3]
return(df_stat)
} 5. Create Coin Pairs Function
Description
Two sets of currency pairs are examined: currency pairs where USDT is the quote currency and currency pairs where BTC is the quote currency. All combinations of coins are created within a given quote currency. Combinations that consist of the coin with itself are removed. The function returns a dataframe containing the coin pairs.
Arguments
quote_currency: A string indicating the quote currency of the currency pairs. Can take values USDT or BTC.
create_pairs <- function(quote_currency) {
if (quote_currency == "USDT") {
coin_list <- c("USDT_BTC", "USDT_DASH", "USDT_ETH", "USDT_LTC", "USDT_REP", "USDT_XMR", "USDT_ZEC")
}
if (quote_currency == "BTC") {
coin_list <- c("BTC_DASH", "BTC_ETH", "BTC_LTC", "BTC_REP", "BTC_XEM", "BTC_XMR", "BTC_ZEC")
}
coin_pairs <- expand.grid(coin_list, coin_list) %>%
rename(coin_y = Var1,
coin_x = Var2) %>%
filter(coin_y != coin_x) %>%
mutate_if(is.factor, as.character) %>%
as_tibble()
return(coin_pairs)
} 6. Test Coin Pairs Function
Description
Test for cointegration between each coin pair generated by the create_pairs() function. The test for cointegration is performed by the test_cointegration() function. The function returns a dataframe containing the coin pairs and the ADF test statistic resulting from testing cointegration between each coin pair.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pairs.
coin_pairs: A dataframe generated by create_pairs().
test_pairs <- function(train, coin_pairs) {
adf_stat <- c()
for (n in 1:nrow(coin_pairs)) {
coin_y <- coin_pairs[[n, "coin_y"]]
coin_x <- coin_pairs[[n, "coin_x"]]
cointegration_results <- test_cointegration(coin_y = train[[coin_y]], coin_x = train[[coin_x]])
adf_stat <- c(adf_stat, cointegration_results)
}
df <- coin_pairs %>%
mutate(adf_stat = adf_stat) %>%
arrange(adf_stat)
return(df)
} 7. Select Coin Pairs Function
Description
Select cointegrated coin pairs to be used in a mean reversion strategy. The current coin selection logic is to select all coins where the ADF test statistic is less than -2.57.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pair.
coin_pairs: A dataframe generated by create_pairs().
select_pairs <- function(train, coin_pairs) {
set.seed(5)
df <- test_pairs(train = train, coin_pairs = coin_pairs) %>%
filter(adf_stat <= -3.43)
return(df)
} 8. Generate Signals Function
Description
Generate trading signals that indicate the current position in the spread formed by a linear combination of coin y and coin x. A signal of +1 indicates a long position in the spread, 0 indicates a flat position, and -1 indicates a short position in the spread. Signals are generated for the test set using a model trained on the training set.
The current trading logic is perform a linear regression of log(coin y) on log(coin x) using the training set. A spread is then calculated in the test set using the fitted hedge ratio and intercept from the regression. The z-score of the spread is then calculated using the mean and standard deviation from the training set. A position is entered when the z-score reaches +2 or -2 and is exited when the z-score reaches 0. Also exits losing positions when the z-score reaches +4 or -4 and re-enters the position when when it returns to within the +4 or -4 range.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pair.
test: A dataframe generated by prepare_data() that represents the test set for the coin pair.
coin_y: A string indicating the dependent coin in the coin pair regression.
coin_x: A string indicating the independent coin in the coin pair regression.
threshold_z: A number indicating the absolute value of the z-score threshold for entering a position in the spread.
generate_signals <- function(train, test, coin_y, coin_x, threshold_z) {
model <- lm(log(train[[coin_y]]) ~ log(train[[coin_x]]))
intercept <- coef(model)[1]
hedge_ratio <- coef(model)[2]
df_signals <- test %>%
mutate(spread = log(test[[coin_y]]) - log(test[[coin_x]]) * hedge_ratio - intercept,
spread_z = (spread - mean(model[["residuals"]])) / sd(model[["residuals"]]),
lag_spread_z = lag(spread_z, 1),
signal_long = ifelse(lag_spread_z <= 0 & lag_spread_z > -1, 0.25, 0),
signal_long = ifelse(lag_spread_z <= -1 & lag_spread_z > -2, 0.50, signal_long),
signal_long = ifelse(lag_spread_z <= -2 & lag_spread_z > -3, 0.75, signal_long),
signal_long = ifelse(lag_spread_z <= -3 & lag_spread_z > -4, 1.00, signal_long),
signal_long = ifelse(lag_spread_z <= -4, 0, signal_long),
signal_short = ifelse(lag_spread_z >= 0 & lag_spread_z < 1, -0.25, 0),
signal_short = ifelse(lag_spread_z >= 1 & lag_spread_z < 2, -0.50, signal_short),
signal_short = ifelse(lag_spread_z >= 2 & lag_spread_z < 3, -0.75, signal_short),
signal_short = ifelse(lag_spread_z >= 3 & lag_spread_z < 4, -1.00, signal_short),
signal_short = ifelse(lag_spread_z >= 4, 0, signal_short),
signal = signal_long + signal_short,
signal = ifelse(is.na(signal), 0, signal))
return(df_signals[["signal"]])
} 9. Backtest Pair Function
Description
Calculate the return of a cointegration-based mean reversion trading strategy using coin y and coin x.
The current backtesting logic uses signals generated by generate_signals(). The coin_y_return and coin_x_return indicate the one period percentage return of each coin. The coin_y_position and coin_x_position indicate the market value in USD in each coin. coin_y_pnl and coin_x_pnl indicate the USD value of the profit and loss for each coin. The combined_position indicates the gross market value of the combined positions.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pair.
test: A dataframe generated by prepare_data() that represents the test set for the coin pair.
coin_y: A string indicating the dependent coin in the coin pair regression.
coin_x: A string indicating the independent coin in the coin pair regression.
threshold_z: A number indicating the absolute value of the z-score threshold for entering a position in the spread.
backtest_pair <- function(train, test, coin_y, coin_x, threshold_z) {
model <- lm(log(train[[coin_y]]) ~ log(train[[coin_x]]))
intercept <- coef(model)[1]
hedge_ratio <- coef(model)[2]
df_backtest <- test %>%
mutate(signal = generate_signals(train = train,
test = test,
coin_y = coin_y,
coin_x = coin_x,
threshold_z = threshold_z),
coin_y_return = test[[coin_y]] / lag(test[[coin_y]], 1) - 1,
coin_x_return = test[[coin_x]] / lag(test[[coin_x]], 1) - 1,
coin_y_position = signal * 1 * 1,
coin_x_position = signal * hedge_ratio * -1,
coin_y_pnl = lag(coin_y_position, 1) * coin_y_return,
coin_x_pnl = lag(coin_x_position, 1) * coin_x_return,
combined_position = abs(coin_y_position) + abs(coin_x_position),
combined_pnl = coin_y_pnl + coin_x_pnl,
combined_return = combined_pnl / (1 + hedge_ratio)) %>%
mutate_all(funs(ifelse(is.na(.), 0, .))) %>%
mutate(return_pair = cumprod(1 + combined_return))
return(df_backtest[["return_pair"]])
} 10. Backtest Strategy Function
Description
Calculate the return of a cointegration-based mean reversion trading strategy using an equally weighted portfolio of cointegrated coin pairs.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pair.
test: A dataframe generated by prepare_data() that represents the test set for the coin pair.
selected_pairs: A dataframe generated by select_coins() that represents a set of cointegrated coin pairs.
backtest_strategy <- function(train, test, selected_pairs, threshold_z) {
if (nrow(selected_pairs) == 0) {
return(1)
}
df <- tibble()
for (i in 1:nrow(selected_pairs)) {
single_pair <- tibble(
return_pair = backtest_pair(train = train,
test = test,
coin_y = selected_pairs[["coin_y"]][i],
coin_x = selected_pairs[["coin_x"]][i],
threshold_z = threshold_z),
coin_y = selected_pairs[["coin_y"]][i],
coin_x = selected_pairs[["coin_x"]][i],
date_time = test[["date_time"]]
)
df <- bind_rows(df, single_pair)
}
df <- df %>%
group_by(date_time) %>%
summarise(return_strategy = mean(return_pair))
return(df[["return_strategy"]])
} 11. Plot Single Function
Description
Create plots of a cointegration-based mean reversion trading strategy of a single coin pair conprised of coin y and coin x. There are two plots created by this function. The first plot displays the spread transformed into z-score with three red lines at -2, 0, and 2. A green line indicates the signal which can take values -1, 0, and +1. The second plot displays the cumulative return of the model in blue. Two additional lines show the buy and hold return of coin y and coin x as red and green lines, respectively.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pair.
test: A dataframe generated by prepare_data() that represents the test set for the coin pair.
coin_y: A string indicating the dependent coin in the coin pair regression.
coin_x: A string indicating the independent coin in the coin pair regression.
threshold_z: A number indicating the absolute value of the z-score threshold for entering a position in the spread.
plot_single <- function(train, test, coin_y, coin_x, threshold_z) {
model <- lm(log(train[[coin_y]]) ~ log(train[[coin_x]]))
intercept <- coef(model)[1]
hedge_ratio <- coef(model)[2]
df_plot <- test %>%
mutate(spread = log(test[[coin_y]]) - log(test[[coin_x]]) * hedge_ratio - intercept,
spread_z = (spread - mean(model[["residuals"]])) / sd(model[["residuals"]]),
signal = generate_signals(train = train,
test = test,
coin_y = coin_y,
coin_x = coin_x,
threshold_z = threshold_z),
return_pair = backtest_pair(train = train,
test = test,
coin_y = coin_y,
coin_x = coin_x,
threshold_z = threshold_z),
return_buyhold_y = test[[coin_y]] / test[[coin_y]][1],
return_buyhold_x = test[[coin_x]] / test[[coin_x]][1])
print(summary(model))
print(ggplot(df_plot, aes(x = date_time)) +
geom_line(aes(y = spread_z, colour = "Spread Z"), size = 1) +
geom_line(aes(y = signal, colour = "Signal"), size = 0.5) +
geom_hline(yintercept = 0, colour = "red", alpha = 0.5) +
geom_hline(yintercept = 2, colour = "red", alpha = 0.5) +
geom_hline(yintercept = -2, colour = "red", alpha = 0.5) +
scale_color_manual(name = "Series",
values = c("Spread Z" = "blue",
"Signal" = "green")) +
labs(title = "Spread vs Trading Signal",
subtitle = str_c(coin_y, " and ", coin_x),
x = "Date",
y = "Spread and Signal"))
print(ggplot(df_plot, aes(x = date_time)) +
geom_line(aes(y = return_pair, colour = "Model"), size = 1) +
geom_line(aes(y = return_buyhold_y, colour = "Coin Y"), size = 0.5, alpha = 0.4) +
geom_line(aes(y = return_buyhold_x, colour = "Coin X"), size = 0.5, alpha = 0.4) +
geom_hline(yintercept = 1, colour = "black") +
scale_color_manual(name = "Return",
values = c("Model" = "darkblue",
"Coin Y" = "darkred",
"Coin X" = "darkgreen")) +
labs(title = "Model Return vs Buy Hold Return",
subtitle = str_c(coin_y, " and ", coin_x),
x = "Date",
y = "Cumulative Return"))
} 12. Plot Many Function
Description
Create many plots by calling the plot_single() function multiple times. Also creates a plot showing the results of the overall strategy. Creates a train and test set surrounding a cutoff date and creates plot for the top 10 selected coins ranked by their ADF statistic.
Arguments
pricing_data: A dataframe containing pricing data from Poloneix gathered in tidy format.
time_resolution: The number of seconds that each observation spans. Takes values 300, 900, 1800, 7200, 14400, and 86400.
cutoff_date: A data representing the cutoff date between the train and test sets.
train_window: A period object from the lubridate package representing the length of time the train set covers.
test_window: A period object from lubridate package representing the length of time the the test set covers. threshold_z: A number indicating the absolute value of the z-score threshold for entering a position in the spread.
plot_many <- function(pricing_data, time_resolution, cutoff_date, train_window, test_window, threshold_z) {
train <- prepare_data(pricing_data = pricing_data,
time_resolution = time_resolution,
start_date = as.Date(cutoff_date) - train_window,
end_date = as.Date(cutoff_date))
test <- prepare_data(pricing_data = pricing_data,
time_resolution = time_resolution,
start_date = as.Date(cutoff_date),
end_date = as.Date(cutoff_date) + test_window)
selected_pairs <- select_pairs(train = train,
coin_pairs = create_pairs(quote_currency = quote_currency))
if (nrow(selected_pairs) == 0) {
return("No coin pairs selected.")
}
print(selected_pairs)
for (i in 1:min(10, nrow(selected_pairs))) {
plot_single(train = train,
test = test,
coin_y = selected_pairs[["coin_y"]][i],
coin_x = selected_pairs[["coin_x"]][i],
threshold_z = threshold_z)
}
test <- test %>%
mutate(return_strategy = backtest_strategy(train = train,
test = .,
selected_pairs = selected_pairs,
threshold_z = threshold_z))
ggplot(test, aes(x = date_time)) +
geom_line(aes(y = return_strategy, colour = "Strategy"), size = 1) +
geom_line(aes(y = USDT_BTC / USDT_BTC[1], colour = "USDT_BTC"), size = 0.5, alpha = 0.4) +
geom_hline(yintercept = 1, colour = "black") +
scale_color_manual(name = "Return",
values = c("Strategy" = "darkblue",
"USDT_BTC" = "darkred")) +
labs(title = "Strategy Return vs Buy Hold Return",
x = "Date",
y = "Cumulative Return")
} 13. Set Parameters
quote_currency <- "BTC"
time_resolution <- 900
train_window <- days(32)
test_window <- days(16)
test_by <- "16 days"
threshold_z <- 2 14. Cross Validation September 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-09-01",
train_window = train_window,
test_window = test_window,
threshold_z = threshold_z) ## # A tibble: 11 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 BTC_REP BTC_ZEC -4.963602
## 2 BTC_ZEC BTC_REP -4.867776
## 3 BTC_ETH BTC_ZEC -4.129661
## 4 BTC_XEM BTC_ZEC -3.828771
## 5 BTC_ZEC BTC_ETH -3.803343
## 6 BTC_ETH BTC_XEM -3.770694
## 7 BTC_ETH BTC_REP -3.689461
## 8 BTC_XEM BTC_ETH -3.640334
## 9 BTC_ZEC BTC_XEM -3.612975
## 10 BTC_ZEC BTC_LTC -3.504784
## 11 BTC_REP BTC_ETH -3.465348
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.17650 -0.03399 -0.00319 0.02588 0.25218
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.724288 0.023547 -115.7 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.866522 0.008338 103.9 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05422 on 3071 degrees of freedom
## Multiple R-squared: 0.7786, Adjusted R-squared: 0.7785
## F-statistic: 1.08e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.230094 -0.035929 0.004614 0.040786 0.160106
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.823132 0.044705 40.78 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.898522 0.008646 103.92 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05521 on 3071 degrees of freedom
## Multiple R-squared: 0.7786, Adjusted R-squared: 0.7785
## F-statistic: 1.08e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.143948 -0.028154 0.003173 0.033042 0.080990
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.178540 0.018659 -63.16 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.487972 0.006607 73.85 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04296 on 3071 degrees of freedom
## Multiple R-squared: 0.6398, Adjusted R-squared: 0.6397
## F-statistic: 5454 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.209404 -0.059042 0.006272 0.059956 0.243530
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.28043 0.03761 -193.60 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.82288 0.01332 61.79 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08659 on 3071 degrees of freedom
## Multiple R-squared: 0.5542, Adjusted R-squared: 0.5541
## F-statistic: 3818 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.11038 -0.06027 -0.01465 0.05830 0.19164
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.52881 0.04538 11.65 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.31109 0.01775 73.85 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07042 on 3071 degrees of freedom
## Multiple R-squared: 0.6398, Adjusted R-squared: 0.6397
## F-statistic: 5454 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.163273 -0.040941 0.009563 0.034808 0.135724
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.34669 0.06472 20.81 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.40637 0.00674 60.29 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04844 on 3071 degrees of freedom
## Multiple R-squared: 0.5421, Adjusted R-squared: 0.5419
## F-statistic: 3635 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.159000 -0.032542 -0.002298 0.041504 0.138749
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.328620 0.041764 -7.868 0.00000000000000493 ***
## log(train[[coin_x]]) 0.430770 0.008078 53.330 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05158 on 3071 degrees of freedom
## Multiple R-squared: 0.4808, Adjusted R-squared: 0.4806
## F-statistic: 2844 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.205722 -0.070606 -0.007659 0.065672 0.251793
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.19349 0.05656 -109.51 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.33394 0.02212 60.29 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08776 on 3071 degrees of freedom
## Multiple R-squared: 0.5421, Adjusted R-squared: 0.5419
## F-statistic: 3635 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.190054 -0.064251 -0.005459 0.053331 0.207766
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.6459 0.1047 34.83 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.6735 0.0109 61.79 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07834 on 3071 degrees of freedom
## Multiple R-squared: 0.5542, Adjusted R-squared: 0.5541
## F-statistic: 3818 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.164558 -0.041649 -0.007901 0.034900 0.203965
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.406535 0.035781 11.36 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.740433 0.008203 90.26 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06139 on 3071 degrees of freedom
## Multiple R-squared: 0.7262, Adjusted R-squared: 0.7261
## F-statistic: 8147 on 1 and 3071 DF, p-value: < 0.00000000000000022
15. Cross Validation August 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-08-01",
train_window = train_window,
test_window = test_window,
threshold_z = threshold_z) ## # A tibble: 9 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 BTC_ETH BTC_ZEC -5.602468
## 2 BTC_ZEC BTC_ETH -5.486184
## 3 BTC_ETH BTC_REP -4.189460
## 4 BTC_ZEC BTC_REP -3.981877
## 5 BTC_REP BTC_ETH -3.942809
## 6 BTC_REP BTC_ZEC -3.883980
## 7 BTC_DASH BTC_XMR -3.677335
## 8 BTC_XEM BTC_XMR -3.643599
## 9 BTC_XMR BTC_DASH -3.472615
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.098475 -0.016144 -0.001821 0.013377 0.129858
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.682007 0.006483 -105.2 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.708955 0.002631 269.4 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02793 on 3071 degrees of freedom
## Multiple R-squared: 0.9594, Adjusted R-squared: 0.9594
## F-statistic: 7.26e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.173140 -0.019467 0.000125 0.024995 0.129435
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.823251 0.012193 67.52 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.353284 0.005022 269.45 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03859 on 3071 degrees of freedom
## Multiple R-squared: 0.9594, Adjusted R-squared: 0.9594
## F-statistic: 7.26e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.141739 -0.028546 -0.003488 0.027501 0.163335
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.030387 0.024938 41.32 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.721545 0.005206 138.60 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05148 on 3071 degrees of freedom
## Multiple R-squared: 0.8622, Adjusted R-squared: 0.8621
## F-statistic: 1.921e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.233523 -0.025842 -0.000285 0.043309 0.235245
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.376439 0.031563 75.29 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.009625 0.006589 153.24 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06515 on 3071 degrees of freedom
## Multiple R-squared: 0.8843, Adjusted R-squared: 0.8843
## F-statistic: 2.348e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.205892 -0.038271 -0.005142 0.044267 0.174785
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.890978 0.020929 -90.35 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.194903 0.008621 138.60 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06625 on 3071 degrees of freedom
## Multiple R-squared: 0.8622, Adjusted R-squared: 0.8621
## F-statistic: 1.921e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.227419 -0.039564 -0.008293 0.029624 0.222612
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.635217 0.014085 -187.1 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.875909 0.005716 153.2 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06069 on 3071 degrees of freedom
## Multiple R-squared: 0.8843, Adjusted R-squared: 0.8843
## F-statistic: 2.348e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.122832 -0.042883 0.005057 0.030852 0.151922
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.01629 0.05052 0.322 0.747
## log(train[[coin_x]]) 0.64442 0.01230 52.410 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04625 on 3071 degrees of freedom
## Multiple R-squared: 0.4721, Adjusted R-squared: 0.472
## F-statistic: 2747 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.237287 -0.044656 0.003621 0.050134 0.193754
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.83351 0.07513 -90.96 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.70534 0.01829 38.58 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06878 on 3071 degrees of freedom
## Multiple R-squared: 0.3264, Adjusted R-squared: 0.3262
## F-statistic: 1488 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.138292 -0.029814 -0.005207 0.040320 0.110065
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.18042 0.03679 -59.27 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.73266 0.01398 52.41 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04931 on 3071 degrees of freedom
## Multiple R-squared: 0.4721, Adjusted R-squared: 0.472
## F-statistic: 2747 on 1 and 3071 DF, p-value: < 0.00000000000000022
16. Cross Validation July 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-07-01",
train_window = train_window,
test_window = test_window,
threshold_z = threshold_z) ## # A tibble: 3 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 BTC_XMR BTC_REP -4.731286
## 2 BTC_REP BTC_XMR -4.559391
## 3 BTC_XMR BTC_ETH -3.477126
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.105170 -0.020197 -0.000205 0.024449 0.147395
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.28443 0.03367 -67.84 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.37806 0.00751 50.34 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03532 on 3071 degrees of freedom
## Multiple R-squared: 0.4522, Adjusted R-squared: 0.452
## F-statistic: 2535 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.204531 -0.028456 0.006383 0.036683 0.169144
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.27585 0.09454 2.918 0.00355 **
## log(train[[coin_x]]) 1.19597 0.02376 50.345 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06281 on 3071 degrees of freedom
## Multiple R-squared: 0.4522, Adjusted R-squared: 0.452
## F-statistic: 2535 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.097654 -0.023953 -0.003966 0.023561 0.188412
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.725166 0.010454 -356.3 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.116588 0.004779 24.4 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04367 on 3071 degrees of freedom
## Multiple R-squared: 0.1623, Adjusted R-squared: 0.1621
## F-statistic: 595.1 on 1 and 3071 DF, p-value: < 0.00000000000000022
17. Cross Validation June 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-06-01",
train_window = train_window,
test_window = test_window,
threshold_z = threshold_z) ## # A tibble: 9 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 BTC_REP BTC_DASH -5.585866
## 2 BTC_DASH BTC_REP -5.575748
## 3 BTC_XMR BTC_ZEC -4.142801
## 4 BTC_XMR BTC_REP -3.959087
## 5 BTC_REP BTC_XMR -3.803859
## 6 BTC_XMR BTC_DASH -3.718922
## 7 BTC_DASH BTC_XMR -3.583567
## 8 BTC_XMR BTC_ETH -3.580314
## 9 BTC_ZEC BTC_ETH -3.540196
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.303124 -0.046684 0.002596 0.039329 0.279482
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.86207 0.02944 -63.26 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.94355 0.01012 93.21 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06565 on 3071 degrees of freedom
## Multiple R-squared: 0.7389, Adjusted R-squared: 0.7388
## F-statistic: 8689 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.251513 -0.044657 -0.003911 0.043419 0.280357
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.699322 0.038690 18.07 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.783065 0.008401 93.21 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05981 on 3071 degrees of freedom
## Multiple R-squared: 0.7389, Adjusted R-squared: 0.7388
## F-statistic: 8689 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.185801 -0.044324 -0.007035 0.027913 0.263842
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.423057 0.012484 -274.20 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.238733 0.004615 51.73 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06513 on 3071 degrees of freedom
## Multiple R-squared: 0.4657, Adjusted R-squared: 0.4655
## F-statistic: 2676 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.170510 -0.045684 -0.005116 0.038648 0.269216
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.19105 0.04666 -46.96 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.40727 0.01013 40.20 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07212 on 3071 degrees of freedom
## Multiple R-squared: 0.3448, Adjusted R-squared: 0.3446
## F-statistic: 1616 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.21261 -0.07797 -0.01731 0.05047 0.32412
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.16127 0.08565 -13.56 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.84665 0.02106 40.20 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.104 on 3071 degrees of freedom
## Multiple R-squared: 0.3448, Adjusted R-squared: 0.3446
## F-statistic: 1616 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.14842 -0.04589 -0.00320 0.03037 0.34510
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.81142 0.03291 -85.44 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.43177 0.01132 38.16 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07338 on 3071 degrees of freedom
## Multiple R-squared: 0.3216, Adjusted R-squared: 0.3214
## F-statistic: 1456 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.22882 -0.07094 -0.02948 0.07389 0.27235
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.12311 0.07940 1.551 0.121
## log(train[[coin_x]]) 0.74491 0.01952 38.158 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09639 on 3071 degrees of freedom
## Multiple R-squared: 0.3216, Adjusted R-squared: 0.3214
## F-statistic: 1456 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.17106 -0.04795 -0.01283 0.02951 0.32739
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.388707 0.018289 -185.28 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.242131 0.006521 37.13 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07402 on 3071 degrees of freedom
## Multiple R-squared: 0.3099, Adjusted R-squared: 0.3096
## F-statistic: 1379 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.49026 -0.05646 0.01091 0.06882 0.52385
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.28478 0.03251 8.76 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.06460 0.01159 91.85 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1316 on 3071 degrees of freedom
## Multiple R-squared: 0.7331, Adjusted R-squared: 0.7331
## F-statistic: 8437 on 1 and 3071 DF, p-value: < 0.00000000000000022
18. Cross Validation May 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-05-01",
train_window = train_window,
test_window = test_window,
threshold_z = threshold_z) ## # A tibble: 18 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 BTC_REP BTC_ETH -5.006093
## 2 BTC_LTC BTC_XEM -4.747154
## 3 BTC_DASH BTC_ETH -4.634350
## 4 BTC_DASH BTC_REP -4.496507
## 5 BTC_DASH BTC_ZEC -4.460635
## 6 BTC_ETH BTC_REP -4.405342
## 7 BTC_LTC BTC_ZEC -4.340114
## 8 BTC_REP BTC_ZEC -4.181057
## 9 BTC_ZEC BTC_ETH -3.922604
## 10 BTC_LTC BTC_XMR -3.921014
## 11 BTC_LTC BTC_REP -3.901344
## 12 BTC_LTC BTC_ETH -3.855233
## 13 BTC_ZEC BTC_REP -3.815340
## 14 BTC_XMR BTC_LTC -3.674490
## 15 BTC_ETH BTC_ZEC -3.608956
## 16 BTC_REP BTC_DASH -3.562364
## 17 BTC_DASH BTC_XEM -3.479815
## 18 BTC_LTC BTC_DASH -3.439666
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.243207 -0.043248 -0.004972 0.042142 0.283352
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.26795 0.03746 -60.55 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.74116 0.01174 63.15 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07188 on 3071 degrees of freedom
## Multiple R-squared: 0.5649, Adjusted R-squared: 0.5648
## F-statistic: 3987 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.64070 -0.07878 -0.01065 0.10224 0.33519
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.295022 0.083067 3.552 0.000389 ***
## log(train[[coin_x]]) 0.462342 0.007707 59.992 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1346 on 3071 degrees of freedom
## Multiple R-squared: 0.5396, Adjusted R-squared: 0.5394
## F-statistic: 3599 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.40788 -0.02868 0.00549 0.03510 0.18551
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.71347 0.03286 -21.71 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.66051 0.01030 64.15 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06305 on 3071 degrees of freedom
## Multiple R-squared: 0.5726, Adjusted R-squared: 0.5725
## F-statistic: 4115 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43255 -0.04479 -0.00292 0.03431 0.34540
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.90420 0.06542 -13.82 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.41362 0.01412 29.29 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08527 on 3071 degrees of freedom
## Multiple R-squared: 0.2184, Adjusted R-squared: 0.2181
## F-statistic: 857.9 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.37359 -0.04167 -0.01106 0.03466 0.26104
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.72366 0.04622 -15.66 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.72872 0.01606 45.37 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07463 on 3071 degrees of freedom
## Multiple R-squared: 0.4013, Adjusted R-squared: 0.4011
## F-statistic: 2058 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.23111 -0.03741 -0.01738 0.02099 0.27348
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.34105 0.05592 6.099 0.0000000012 ***
## log(train[[coin_x]]) 0.76220 0.01207 63.145 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07289 on 3071 degrees of freedom
## Multiple R-squared: 0.5649, Adjusted R-squared: 0.5648
## F-statistic: 3987 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.85383 -0.10088 0.02582 0.12960 0.34575
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.24885 0.12013 -27.05 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.49966 0.04174 11.97 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1939 on 3071 degrees of freedom
## Multiple R-squared: 0.04458, Adjusted R-squared: 0.04427
## F-statistic: 143.3 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.256927 -0.056269 0.000649 0.043824 0.284026
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.10764 0.04979 -42.33 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.87740 0.01730 50.72 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08038 on 3071 degrees of freedom
## Multiple R-squared: 0.4558, Adjusted R-squared: 0.4556
## F-statistic: 2572 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.136863 -0.039752 -0.003195 0.034642 0.235201
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.971391 0.026937 -36.06 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.597421 0.008441 70.77 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05169 on 3071 degrees of freedom
## Multiple R-squared: 0.6199, Adjusted R-squared: 0.6198
## F-statistic: 5009 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.47762 -0.09886 -0.00977 0.10808 0.43601
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -13.9785 0.1758 -79.49 <0.0000000000000002 ***
## log(train[[coin_x]]) -2.2882 0.0433 -52.85 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1436 on 3071 degrees of freedom
## Multiple R-squared: 0.4763, Adjusted R-squared: 0.4761
## F-statistic: 2793 on 1 and 3071 DF, p-value: < 0.00000000000000022
19. Cross Validation April 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-04-01",
train_window = train_window,
test_window = test_window,
threshold_z = threshold_z)## # A tibble: 8 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 BTC_XEM BTC_ZEC -4.121186
## 2 BTC_ZEC BTC_XEM -3.946709
## 3 BTC_REP BTC_ETH -3.923221
## 4 BTC_ETH BTC_REP -3.919118
## 5 BTC_DASH BTC_XMR -3.846020
## 6 BTC_XMR BTC_ZEC -3.725802
## 7 BTC_XMR BTC_DASH -3.692261
## 8 BTC_ZEC BTC_XMR -3.663936
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.42059 -0.03847 0.01868 0.07308 0.25551
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -8.955500 0.018855 -475.0 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.814683 0.005997 135.9 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1103 on 3071 degrees of freedom
## Multiple R-squared: 0.8573, Adjusted R-squared: 0.8573
## F-statistic: 1.846e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.31897 -0.07513 -0.01755 0.06639 0.52712
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.978369 0.089133 100.7 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.052359 0.007746 135.9 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1253 on 3071 degrees of freedom
## Multiple R-squared: 0.8573, Adjusted R-squared: 0.8573
## F-statistic: 1.846e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.20181 -0.04849 -0.01266 0.03608 0.37271
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.953760 0.009316 -317.1 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.577941 0.002548 226.8 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07335 on 3071 degrees of freedom
## Multiple R-squared: 0.9437, Adjusted R-squared: 0.9437
## F-statistic: 5.145e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.57861 -0.06992 0.01310 0.09656 0.35437
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.619085 0.036388 126.9 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.632817 0.007199 226.8 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1233 on 3071 degrees of freedom
## Multiple R-squared: 0.9437, Adjusted R-squared: 0.9437
## F-statistic: 5.145e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.33841 -0.08243 -0.00249 0.07335 0.37893
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.241328 0.035723 90.73 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.443311 0.008526 169.29 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1365 on 3071 degrees of freedom
## Multiple R-squared: 0.9032, Adjusted R-squared: 0.9032
## F-statistic: 2.866e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.24816 -0.04974 -0.01505 0.03430 0.40928
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.637464 0.017595 -93.06 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.813237 0.005596 145.31 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1029 on 3071 degrees of freedom
## Multiple R-squared: 0.873, Adjusted R-squared: 0.873
## F-statistic: 2.112e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.27888 -0.05304 0.01216 0.05960 0.24929
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.432975 0.010447 -232.9 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.625792 0.003697 169.3 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08986 on 3071 degrees of freedom
## Multiple R-squared: 0.9032, Adjusted R-squared: 0.9032
## F-statistic: 2.866e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.43774 -0.05981 0.03444 0.07622 0.33734
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.360900 0.030954 43.97 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.073528 0.007388 145.31 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1183 on 3071 degrees of freedom
## Multiple R-squared: 0.873, Adjusted R-squared: 0.873
## F-statistic: 2.112e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
20. Cross Validation March 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-03-01",
train_window = train_window,
test_window = test_window,
threshold_z = threshold_z) ## # A tibble: 2 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 BTC_XMR BTC_LTC -4.163767
## 2 BTC_LTC BTC_XMR -4.030214
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.096961 -0.023558 -0.006907 0.013749 0.107417
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.741186 0.045673 38.12 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.101011 0.008171 134.75 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03604 on 3071 degrees of freedom
## Multiple R-squared: 0.8553, Adjusted R-squared: 0.8553
## F-statistic: 1.816e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.082026 -0.012154 0.006332 0.019831 0.095291
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.161233 0.025446 -84.94 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.776862 0.005765 134.75 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03027 on 3071 degrees of freedom
## Multiple R-squared: 0.8553, Adjusted R-squared: 0.8553
## F-statistic: 1.816e+04 on 1 and 3071 DF, p-value: < 0.00000000000000022
21. Cross Validation February 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-02-01",
train_window = train_window,
test_window = test_window,
threshold_z = threshold_z) ## # A tibble: 3 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 BTC_REP BTC_ETH -4.550570
## 2 BTC_ETH BTC_REP -3.841857
## 3 BTC_REP BTC_ZEC -3.523153
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.102880 -0.034125 -0.004815 0.026554 0.179239
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.644839 0.032683 -80.92 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.600623 0.007245 82.90 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04532 on 3071 degrees of freedom
## Multiple R-squared: 0.6911, Adjusted R-squared: 0.691
## F-statistic: 6872 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.198335 -0.037258 0.008305 0.046103 0.132195
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.65058 0.07432 22.21 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.15069 0.01388 82.90 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06274 on 3071 degrees of freedom
## Multiple R-squared: 0.6911, Adjusted R-squared: 0.691
## F-statistic: 6872 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.25900 -0.01622 0.02158 0.05104 0.17160
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.46839 0.05429 -82.31 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.29221 0.01792 16.31 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07824 on 3071 degrees of freedom
## Multiple R-squared: 0.07968, Adjusted R-squared: 0.07938
## F-statistic: 265.9 on 1 and 3071 DF, p-value: < 0.00000000000000022
22. Cross Validation January 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-01-01",
train_window = train_window,
test_window = test_window,
threshold_z = threshold_z) ## # A tibble: 5 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 BTC_XEM BTC_ETH -3.913761
## 2 BTC_DASH BTC_XEM -3.861305
## 3 BTC_REP BTC_ETH -3.843512
## 4 BTC_XEM BTC_DASH -3.827549
## 5 BTC_REP BTC_ZEC -3.485578
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.130263 -0.042095 -0.000095 0.036790 0.154270
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.737010 0.038216 -254.79 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.564951 0.008219 68.73 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.05436 on 3071 degrees of freedom
## Multiple R-squared: 0.606, Adjusted R-squared: 0.6059
## F-statistic: 4724 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.088829 -0.033901 -0.003252 0.027641 0.098851
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.930214 0.098801 9.415 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.435756 0.007992 54.527 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03835 on 3071 degrees of freedom
## Multiple R-squared: 0.4919, Adjusted R-squared: 0.4917
## F-statistic: 2973 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.228945 -0.059397 -0.008747 0.064865 0.226972
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.85655 0.05487 -33.84 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.79705 0.01180 67.54 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.07804 on 3071 degrees of freedom
## Multiple R-squared: 0.5977, Adjusted R-squared: 0.5975
## F-statistic: 4562 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.176723 -0.037859 -0.006745 0.041624 0.155113
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.33155 0.09228 -79.45 <0.0000000000000002 ***
## log(train[[coin_x]]) 1.12887 0.02070 54.53 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06173 on 3071 degrees of freedom
## Multiple R-squared: 0.4919, Adjusted R-squared: 0.4917
## F-statistic: 2973 on 1 and 3071 DF, p-value: < 0.00000000000000022
##
## Call:
## lm(formula = log(train[[coin_y]]) ~ log(train[[coin_x]]))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.38003 -0.01884 0.02013 0.05096 0.18371
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.384261 0.022303 -196.58 <0.0000000000000002 ***
## log(train[[coin_x]]) 0.414442 0.007833 52.91 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.08899 on 3071 degrees of freedom
## Multiple R-squared: 0.4769, Adjusted R-squared: 0.4767
## F-statistic: 2799 on 1 and 3071 DF, p-value: < 0.00000000000000022
23. Cross Validation Full
cutoff_dates <- seq(ymd("2017-01-01"), ymd("2017-10-01"), by = test_by)
results <- tibble()
for (cutoff_date in cutoff_dates) {
cutoff_date <- as.Date(cutoff_date)
print(str_c("Cross validating strategy."))
print(str_c("Using train set from ", cutoff_date - train_window , " to ", cutoff_date, "."))
print(str_c("Using test set from ", cutoff_date, " to ", cutoff_date + test_window, "."))
train <- prepare_data(pricing_data = pricing_data,
time_resolution = time_resolution,
start_date = cutoff_date - train_window,
end_date = cutoff_date)
test <- prepare_data(pricing_data = pricing_data,
time_resolution = time_resolution,
start_date = cutoff_date,
end_date = cutoff_date + test_window)
test <- test %>%
mutate(return_strategy =
backtest_strategy(train = train,
test = test,
selected_pairs = select_pairs(train = train, coin_pairs = create_pairs(quote_currency = quote_currency)),
threshold_z = threshold_z),
return_strategy_change = return_strategy / lag(return_strategy, 1) - 1) %>%
mutate_all(funs(ifelse(is.na(.), 0, .)))
results <- bind_rows(results, test)
} ## [1] "Cross validating strategy."
## [1] "Using train set from 2016-11-30 to 2017-01-01."
## [1] "Using test set from 2017-01-01 to 2017-01-17."
## [1] "Cross validating strategy."
## [1] "Using train set from 2016-12-16 to 2017-01-17."
## [1] "Using test set from 2017-01-17 to 2017-02-02."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-01-01 to 2017-02-02."
## [1] "Using test set from 2017-02-02 to 2017-02-18."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-01-17 to 2017-02-18."
## [1] "Using test set from 2017-02-18 to 2017-03-06."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-02-02 to 2017-03-06."
## [1] "Using test set from 2017-03-06 to 2017-03-22."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-02-18 to 2017-03-22."
## [1] "Using test set from 2017-03-22 to 2017-04-07."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-03-06 to 2017-04-07."
## [1] "Using test set from 2017-04-07 to 2017-04-23."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-03-22 to 2017-04-23."
## [1] "Using test set from 2017-04-23 to 2017-05-09."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-04-07 to 2017-05-09."
## [1] "Using test set from 2017-05-09 to 2017-05-25."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-04-23 to 2017-05-25."
## [1] "Using test set from 2017-05-25 to 2017-06-10."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-05-09 to 2017-06-10."
## [1] "Using test set from 2017-06-10 to 2017-06-26."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-05-25 to 2017-06-26."
## [1] "Using test set from 2017-06-26 to 2017-07-12."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-06-10 to 2017-07-12."
## [1] "Using test set from 2017-07-12 to 2017-07-28."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-06-26 to 2017-07-28."
## [1] "Using test set from 2017-07-28 to 2017-08-13."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-07-12 to 2017-08-13."
## [1] "Using test set from 2017-08-13 to 2017-08-29."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-07-28 to 2017-08-29."
## [1] "Using test set from 2017-08-29 to 2017-09-14."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-08-13 to 2017-09-14."
## [1] "Using test set from 2017-09-14 to 2017-09-30."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-08-29 to 2017-09-30."
## [1] "Using test set from 2017-09-30 to 2017-10-16."results <- results %>%
mutate(return_strategy_cumulative = cumprod(1 + return_strategy_change),
date_time = as.POSIXct(date_time, origin = "1970-01-01"))
ggplot(results, aes(x = date_time)) +
geom_line(aes(y = return_strategy_cumulative), colour = "blue", size = 1) +
geom_hline(yintercept = 1, colour = "black") +
labs(title = "Strategy Return vs Buy Hold Return", x = "Date", y = "Cumulative Return") 
print(results[["return_strategy_cumulative"]][nrow(results)]) ## [1] 1.176044